Structures and energies of isolobal (BCO)n and (CH)n cages

The structures and energies of isolobal (CH)n and (BCO)n polyhedral species, computed at the B3LYP density functional theory level, reveal contrasts in behavior. The strain energies of the (BCO)n cages are much smaller. Also unlike the (CH)n cages, the most stable (BCO)n polyhedra (n > or = 10) prefer structures with the largest number of three-membered rings. The planar (or nearly planar) faces of the cage systems were modeled by computations on planar, isoelectronic (CH2)n (Dnh) and (HBCO)n (Cnv) rings. While the strain energies of all the planar carbon rings, relative to the most stable D5h (CH2)5, were large, the strain energies of all the planar (HBCO)n (Cnv) rings were small. Remarkably, the three-membered (HBCO)3 (C3v) ring was the most stable. Finally, large (BCO)n systems prefer tubelike rather than cage structures.     

Electronic structures, vibrational and thermochemical properties of neutral and charged niobium clusters Nb(n), n = 7-12

Geometric and electronic structures, vibrational properties, and relative stabilities of niobium clusters Nb(n), n = 7-12, are studied using both DFT (BPW91 and M06 functionals) and CCSD(T) calculations with the cc-pVnZ-PP basis set. In each cluster, various lower-lying states are very close in energy in such a way that the ground state cannot be unambiguously established by DFT computations. Nb clusters tend to prefer the lowest possible spin state as the ground state, except for Nb(12) ((3)A(g)). The optimal structure of the cluster at a certain size does not simply grow from that of the smaller one by adding an atom randomly. Instead, the Nb clusters prefer a close-packed growth behavior. Nb(10) has a spherically aromatic character, high chemical hardness and large HOMO-LUMO gap. Electron affinities, ionization energies, binding energy per atom, and the stepwise dissociation energies are evaluated. Energetic properties exhibit odd-even oscillations. Comparison with experimental values shows that both BPW91 and M06 functionals are reliable in predicting the EA and IE values, but the BPW91 is deficient in predicting the binding and dissociation energies. We re-examine in particular the experimental far IR spectra previously recorded using the IR-MPD and free electron laser spectrometric techniques and propose novel assignments for Nb(7) and Nb(9) systems. The IR spectra of the anions are also predicted.     

Trends in structural, electronic and energetic properties of bimetallic vanadium-gold clusters Au(n)V with n = 1-14

A systematic quantum chemical investigation on the electronic, geometric and energetic properties of Au(n)V clusters with n = 1-14 in both neutral and anionic states is performed using BP86/cc-pVTZ-PP calculations. Most clusters having an even number of electrons prefer a high spin state. For odd-electron systems, a quartet state is consistently favoured as the ground state up to Au(8)V. The larger sized Au(10)V, Au(12)V and Au(14)V prefer a doublet state. The clusters prefer 2D geometries up to Au(8)V involving a weak charge transfer. The larger systems bear 3D conformations with a more effective electron transfer from Au to V. The lowest-energy structure of a size Au(n)V is built upon the most stable form of Au(n-1)V. During the growth, V is endohedrally doped in order to maximize its coordination numbers and augment the charge transfer. Energetic properties, including the binding energies, embedding energies and second-order energy differences, show that the presence of a V atom enhances considerably the thermodynamic stability of odd-numbered gold clusters but reduces that of even-numbered systems. The atomic shape has an apparently more important effect on the clusters stability than the electronic structure. Especially, if both atomic shape and electronic condition are satisfied, the resulting cluster becomes particularly stable such as the anion Au(12)V(-), which can thus combine with the cation Au(+) to form a superatomic molecule of the type [Au(12)V]Au. Numerous lower-lying electronic states of these clusters are very close in energy, in such a way that DFT computations cannot clearly establish their ground electronic states. Calculated results demonstrate the existence of structural isomers with comparable energy content for several species including Au(9)V, Au(10)V, Au(13)V and Au(14)V.     

叠氮二氢硼多聚体结构和性质的理论研究(英文)

本文采用DFT-B3LYP方法,以不同基组对叠氮二氢硼多聚体(H2BN3)n (n=1-4)进行计算研究.二聚体(H2BN3)2(C2h对称性)中含B2N2平面四元环结构.船式(Cs对称性)和椅式(C3v对称性)三聚体(H2BN3)3的结合能相近(-122 和 -126 kJ·mol-1),其中均含B3N3六元环结构.拥有B4N4八元环结构的四个四聚体的结合能只有稍微差别.与单体相比,簇合物的结构参数变化较大.由ΔG0T可知,298.2 K下单体形成二聚体在热力学上是不利的,而形成三聚体和四聚体是有利的.     

Binding properties of Cu(+/2+)-(glycyl)n glycine complexes (n = 1-3)

The structure, relative energies, and binding energies of the complexes formed by the interaction of Cu+ (d10,1S) and Cu2+ (d9,2D) cations with the (glycyl)n glycine (n = 1-3) oligomers have been theoretically determined by means of density functional methods. The most stable structures of the Cu+ systems present linear dicoordination geometries, in agreement with a recent X-ray absorption spectroscopic study of Cu(I) interacting with model dipeptides. This is attributed to an efficient reduction of metal-ligand repulsion through sd sigma hybridization in dicoordinated linear structures. In contrast, for Cu2+ systems the lowest energy structures are tricoordinated (n = 1), tetracoordinated (n = 2), and pentacoordinated (n = 3). For both copper cations, binding energy values show that the interaction energies increase when the peptide chain is elongated. Differences on the coordination properties of the ligands are discussed according to their length as well as to the electronic configuration of the metal cations, which are compared to the Cu+/2+-glycine systems.     

Density functional theoretical study of a series of binary azides M(N3)n (n = 3, 4)

Geometrical structures of a series of binary azides M(N3)n (M = elements in groups 3 and 13 (n = 3) and in groups 4 and 14 (n = 4)) were investigated at the B3LYP/6-311+G level of theory. Our calculations found that binary group 3 triazides M(N3)3 (M = Sc, Y, La) and binary group 4 tetraazides M(N3)4 (M = Ti, Zr, Hf) turn out to be stable with all frequencies real having a similar linear M-N-NN structural feature, as previously reported for M(N3)4 (M = Ti, Zr, Hf). However, binary azides of group 13 M(N3)3 (M = B, Al, Ga, In, Tl) and group 14 elements M(N3)4 (C, Si, Ge, Sn, Pb) with bent M-N-NN bond angles differ obviously from binary group 3 and 4 azides in geometrical structure. These facts are mainly explained by the difference in electronic density overlap between the central atom and the alpha-N atoms of the azido groups. Two lone-pair electrons on the sp hybridization alpha-N atoms in the binary group 3 and 4 azides donate electron density into two empty d orbitals of the central transition metal atom and a pair of valence bonding electrons, resulting in the alpha-N atoms acting as a tridentate ligand. The sp2 hybridization alpha-N atoms of the binary group 13 and 14 azides only give one valence electron to form one valence bonding electron pair acting virtually as monodentate donors.     

Ruthenium- and palladium-catalyzed enyne cycloisomerizations: differentially stereoselective syntheses of bicyclic structures

Enyne cycloisomerizations can provide an efficient means for forming carbon-carbon bonds. We describe stereoselectively dichotomous enyne cycloisomerizations, entirely dependent on the selection of catalytic manifold. Ruthenium catalysis provides trans-fused bicyclic systems, whereas palladium catalysis provides the analogous cis-fused bicycles. A number of substrates are investigated, and the outcomes ultimately offer a clear mechanistic rationale for these observations.     

硼碳团簇BnC2 (n＝1～6)的理论研究

应用密度泛函理论在B3LYP/6-311＋G(d)水平上研究了硼碳团簇B_nC₂ (n＝1～6)的几何结构、生长机制和相对稳定性. 计算结果表明, 对于n＝2～6的簇, 平面多环状构型为最稳定的结构, 其中C原子分布于环的顶点、有尽可能多的三配位硼原子和尽可能多的B—C键. 碳原子作为杂原子倾向掺杂于团簇的顶点位置, 它的掺杂不改变硼团簇的主体结构. 与平面多环状结构相比, 随着簇尺寸的增大, 三维结构和线性链结构更不稳定. 在低能线性结构中, C原子位于链两侧的第二个位置. 计算的碎片分裂能、递增键能以及HOMO-LUMO能隙表明, B₄C₂为幻数簇.     

Structure and stability of (TiO2)n, (SiO2)n, and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] clusters

Structures, energetics, and vibrational spectra are investigated for small pure (TiO(2))(n), (SiO(2))(n), and mixed Ti(m)Si(n-m)O(2n) [n = 2-5, m = 1 to (n - 1)] oxide clusters by density functional theory (DFT). The BP86/ATZP level of theory is employed to obtain constitutional isomers of the oxide clusters. In accordance with previous studies, our calculations show three-dimensional compact structures are preferred for pure (TiO(2))(n) with oxo-stabilized higher hexavalent states, and linear chain structures are favored for pure (SiO(2))(n) with tetravalent states. However, the herein theoretically first reported mixed Ti(m)Si(n-m)O(2n) oxide clusters prefer either three-dimensional compact or linear chain structures depending upon the stoichiometry of the compound. Vibrational analysis of the important modes of some highly stable structures is provided. Coupled-cluster single and double excitation (with triples) [CCSD(T)] computed energy gaps for the TiO(2) dimers compare well with results from previous study. Excitation energies are computed by use of time-dependent (TD) DFT and equation-of-motion coupled-cluster calculations with singles and doubles (EOM-CCSD) for the most stable isomers.     

Molecular structures and energetics of the (TiO2)n (n = 1-4) clusters and their anions

The (TiO2)n clusters and their anions for n = 1-4 have been studied with coupled cluster theory [CCSD(T)] and density functional theory (DFT). For n > 1, numerous conformations are located for both the neutral and anionic clusters, and their relative energies are calculated at both the DFT and CCSD(T) levels. The CCSD(T) energies are extrapolated to the complete basis set limit for the monomer and dimer and calculated up to the triple-zeta level for the trimer and tetramer. The adiabatic and vertical electron detachment energies of the anionic clusters to the ground and first excited states of the neutral clusters are calculated at both levels and compared with the experimental results. The comparison allows for the definitive assignment of the ground-state structures of the anionic clusters. Anions of the dimer and tetramer are found to have very closely lying conformations within 2 kcal/mol at the CCSD(T) level, whereas that of the trimer does not. In addition, accurate clustering energies and heats of formation are calculated for the neutral clusters and compared with the available experimental data. Estimates of the titanium-oxygen bond energies show that they are stronger than the group VIB transition metal-oxygen bonds except for tungsten. The atomization energies of these clusters display much stronger basis set dependence than the clustering energies. This allows the calculation of more accurate heats of formation for larger clusters on the basis of calculated clustering energies.     

Silicon monohydride clusters Si(n)H (n = 4-10) and their anions: structures, thermochemistry, and electron affinities

The molecular structures, electron affinities, and dissociation energies of the Si(n)H/Si(n)H- (n = 4-10) species have been examined via five hybrid and pure density functional theory (DFT) methods. The basis set used in this work is of double-zeta plus polarization quality with additional diffuse s- and p-type functions, denoted DZP++. The geometries are fully optimized with each DFT method independently. The three different types of neutral-anion energy separations presented in this work are the adiabatic electron affinity (EA(ad)), the vertical electron affinity (EA(vert)), and the vertical detachment energy (VDE). The first Si-H dissociation energies, D(e)(Si(n)H --> Si(n) + H) for neutral Si(n)H and D(e)(Si(n)H- --> Si(n)- + H) for anionic Si(n)H- species, have also been reported. The structures of the ground states of these clusters are traditional H-Si single-bond forms. The ground-state geometries of Si5H, Si6H, Si8H, and Si9H predicted by the DFT methods are different from previous calculations, such as those obtained by Car-Parrinello molecular dynamics and nonorthogonal tight-binding molecular dynamics schemes. The most reliable EA(ad) values obtained at the B3LYP level of theory are 2.59 (Si4H), 2.84 (Si5H), 2.86 (Si6H), 3.19 (Si7H), 3.14 (Si8H), 3.36 (Si9H), and 3.56 (Si10H) eV. The first dissociation energies (Si(n)H --> Si(n) + H) predicted by all of these methods are 2.20-2.29 (Si4H), 2.30-2.83 (Si5H), 2.12-2.41 (Si6H), 1.75-2.03 (Si7H), 2.41-2.72 (Si8H), 1.86-2.11 (Si9H), and 1.92-2.27 (Si10H) eV. For the negatively charged ion clusters (Si(n)H- --> Si(n)- + H), the dissociation energies predicted are 2.56-2.69 (Si4H-), 2.80-3.01 (Si5H-), 2.86-3.06 (Si6H-), 2.80-3.03 (Si7H-), 2.69-2.92 (Si8H-), 2.92-3.18 (Si9H-), and 2.89-3.25 (Si10H-) eV.     

(n‐Nitrophenyl)acetonitrile,with n = 2, 3 and 4

The molecular structures of the three title nitro‐substituted phenyl­aceto­nitriles, C₈H₆N₂O₂, at 123 K show that the mol­ecules are linked together very differently. In the 2‐ and 4‐nitro compounds, there are both O?H and N_cyano?H interactions, whereas the crystal lattice of the 3‐nitro compound is essentially built up by O?H interactions. The O atoms seem to prefer the aromatic H atoms, while the cyano N atoms prefer the methyl­ene H atoms. The phenyl–nitro torsion angles are ?19.83 (13), ?5.69 (12) and ?2.88 (12)°, while the phenyl–cyano­methyl torsion angles are ?62.27 (12), ?147.99 (9) and ?16.75 (14)° in the 2‐, 3‐ and 4‐NO₂‐substituted compounds, respectively.     

Bonding of seven carbonyl groups to a single metal atom: theoretical study of M(CO)n (M = Ti, Zr, Hf; n = 7, 6, 5, 4)

The equilibrium geometries, thermochemistry, and vibrational frequencies of the homoleptic metal-carbonyls of the group 4 elements, M(CO)n (M = Ti, Zr, Hf; n = 7, 6, 5, 4) were predicted using density functional theory. Analogous M(CO)n structures were found for all three metals. The global minima for the 18-electron M(CO)7 molecules are all singlet C(3v) capped octahedra. The global minima for the 16-electron M(CO)6 species are triplet M(CO)6 structures distorted from O(h) symmetry to D(3d) symmetry. However, the corresponding singlet M(CO)6 structures lie within 5 kcal/mol of the triplet global minima. The global minima for M(CO)n (n = 5, 4) are triplet structures derived from the D(3d) distorted octahedral structures of M(CO)6 by removal of one or two CO groups, respectively. Quintet D(3h) trigonal bipyramidal structures for M(CO)5 and singlet T(d) tetrahedral structures for M(CO)4 are also found, as well as higher energy structures for M(CO)6 and M(CO)7 containing a unique CO group bonded to the metal atom through both M-C and M-O bonds. The dissociation energies M(CO)7 --> M(CO)6 + CO are substantial, indicating no fundamental problem in bonding seven CO groups to a single metal atom.     

Chromium-doped germanium clusters CrGen (n = 1-5): geometry, electronic structure, and topology of chemical bonding

The structure and properties of small neutral and cationic CrGen(0,+) clusters, with n from 1 to 5, were investigated using quantum chemical calculations at the CASSCF/CASPT2 and DFT/B3LYP levels. Smaller clusters prefer planar geometries, whereas the lowest-lying electronic states of the neutral CrGe4, CrGe5, and cationic CrGe5+ forms exhibit nonplanar geometries. Most of the clusters considered prefer structures with high-spin ground state and large magnetic moments. Relative to the values obtained for the pure Gen clusters, fragmentation energies of doped CrGen clusters are smaller when n is 3 and 4 and larger when n = 5. The averaged binding energy tends to increase with the increasing number of Ge atoms. For n = 5, the binding energies for Ge5, CrGe5, and CrGe5+ are similar to each other, amounting to approximately 2.5 eV. The Cr atom acts as a general electron donor in neutral CrGen clusters. Electron localization function (ELF) analyses suggest that the chemical bonding in chromium-doped germanium clusters differs from that of their pure or Li-doped counterparts and allow the origin of the inherent high-spin ground state to be understood. The differential DeltaELF picture, obtained in separating both alpha and beta electron components, is consistent with that derived from spin density calculations. For CrGen, n = 2 and 3, a small amount of d-pi back-donation is anticipated within the framework of the proposed bonding model.     

Energy-Minimized Structures and Calculated and Experimental Isomer distributions in the hexaamine-cobalt(III) system [Co(L)2]3+ with the chiral facially-coordinating triamine (l = butane-1,2,4-triamine)

Butane- 1,2,4-triamine (trab) is the smallest tridentate aliphatic unsubstituted chiral triamine. With optically pure trab, there are three, with racemic trab five isomers of [Co(trab)₂]³⁺, One of the five isomers is centrosymmetrical, the others are chiral. For one of the isomers, there are four possible conformations (all combinations of chair and skew boat conformations for the chelate six ring of each ligand), for the others there exist only three independent conformers. All sixteen independent structures have been calculated by strain-energy minimization. The calculated isomer distribution, based on total strain energies corrected with statistical entropy contributions (21%:16%:16%:4%:43%, and 40%:30%:30%, for racemic and optically pure trab, respectively) are in excellent agreement with the experimental data based on HPLC and ¹³C-NMR analyses of equilibrium solutions of the hexaamine-Co(III) compounds prepared by oxygenation of aqueous solutions in presence of activated charcoal. The results are also briefly discussed in relation to possible stereoselectivity upon complexation of optically pure trab and a racemic chiral ligand to a transition-metal center.     

Probing the Lewis acid-catalyzed intramolecular Diels-Alder cyclizations of allylic alkoxy-substituted (Z)-1,3-dienes

[reaction: see text] The Lewis acid-promoted Diels-Alder reaction of (E,Z,E)-trienal 1 provides not only the expected cis-fused cycloadduct 16 but also the trans-fused products 17 and 18. Trans-fused cycloadducts 17 and 18 are also products of the Lewis acid-promoted cyclization of (E,Z,E)-trienyl acetal 2. These products presumably derive from a stepwise cyclization pathway.     

Structures and spectra of Na(NH3) n=1,2

Geometric structures and the energies for the ground and several excited electronic states of a sodium atom bound with one or two ammonia molecules are presented. All self consistent field (SCF) calculations are performed with extended basis sets. Geometry optimization and one electron properties have been performed within the SCF approximation. Excited states have been calculated with the multi-configuration SCF (MCSCF) technique. This system may be viewed as a precursor to solvation in a macroscopic system. The excited state calculations provide important information for spectroscopic studies of these complexes.     

Geometries, stabilities, and electronic properties of different-sized ZrSi(n) (n=1-16) clusters: a density-functional investigation

The ZrSi(n) (n=1-16) clusters with different spin configurations have been systematically investigated by using the density-functional approach. The total energies, equilibrium geometries, growth-pattern mechanisms, natural population analysis, etc., are discussed. The equilibrium structures of different-sized ZrSi(n) clusters can be determined by two evolution patterns. Theoretical results indicate that the most stable ZrSi(n) (n=1-7) geometries, except ZrSi3, keep the analogous frameworks as the lowest-energy or the second lowest-energy Si(n+1) clusters. However, for large ZrSi(n) (n=8-16) clusters, Zr atom obviously disturbs the framework of silicon clusters, and the localized position of the transition-metal (TM) Zr atom gradually varies from the surface insertion site to the concave site of the open silicon cage and to the encapsulated site of the sealed silicon cage. It should be mentioned that the lowest-energy sandwich-like ZrSi12 geometry is not a sealed structure and appears irregular as compared with other TM@Si12 (TM = Re,Ni). The growth patterns of ZrSi(n) (n=1-16) clusters are concerned showing the Zr-encapsulated structures as the favorable geometries. In addition, the calculated fragmentation energies of the ZrSi(n) (n=1-16) clusters manifest that the magic numbers of stabilities are 6, 8, 10, 14, and 16, and that the fullerene-like ZrSi16 is the most stable structure, which is in good agreement with the calculated atomic binding energies of ZrSi(n) (n=8-16) and with available experimental and theoretical results. Natural population analysis shows that the natural charge population of Zr atom in the most stable ZrSi(n) (n=1-16) structures exactly varies from positive to negative at the critical-sized ZrSi8 cluster; furthermore, the charge distribution around the Zr atom appears clearly covalent in character for the small- or middle-sized clusters and metallic in character for the large-sized clusters. Finally, the properties of frontier orbitals and polarizabilities of ZrSi(n) are also discussed.     

Theoretical study of Al(n) and Al(n)O (n = 2-10) clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.     

Structure and stability of coinage metal fluoride and chloride clusters (MnFn and MnCln,M = Cu,Ag, or Au; n = 1–6)

Calculations in the framework of the density functional theory are performed to study the lowest‐energy isomers of coinage metal fluoride and chloride clusters (M_nF_n, M_nCl_n, M = Cu, Ag, or Au, n = 1–6). For all calculated species starting from the trimers the most stable structures are found to be cyclic arrangements. However, planar rings are favored in the case of metal fluorides whereas metal chlorides prefer nonplanar cycles. Calculated bond lengths and infrared frequencies are compared with the available experimental data. The nature of the bonding, involving both covalent and ionic contributions, is characterized. The stability and the fragmentation are also investigated. Trimers are found to be particularly stable when considering the Gibbs free energies. © 2012 Wiley Periodicals, Inc.